From pycyn@aol.com Wed May 01 11:55:10 2002 Return-Path: X-Sender: Pycyn@aol.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-8_0_3_1); 1 May 2002 18:55:09 -0000 Received: (qmail 99900 invoked from network); 1 May 2002 18:55:09 -0000 Received: from unknown (66.218.66.217) by m10.grp.scd.yahoo.com with QMQP; 1 May 2002 18:55:09 -0000 Received: from unknown (HELO imo-d09.mx.aol.com) (205.188.157.41) by mta2.grp.scd.yahoo.com with SMTP; 1 May 2002 18:55:09 -0000 Received: from Pycyn@aol.com by imo-d09.mx.aol.com (mail_out_v32.5.) id r.191.65c92d9 (2615) for ; Wed, 1 May 2002 14:55:06 -0400 (EDT) Message-ID: <191.65c92d9.2a01940a@aol.com> Date: Wed, 1 May 2002 14:55:06 EDT Subject: Re: [lojban] cipja'o To: lojban@yahoogroups.com MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="part1_191.65c92d9.2a01940a_boundary" X-Mailer: AOL 7.0 for Windows US sub 10500 From: pycyn@aol.com X-Yahoo-Group-Post: member; u=2455001 X-Yahoo-Profile: kaliputra --part1_191.65c92d9.2a01940a_boundary Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit In a message dated 5/1/2002 9:05:48 AM Central Daylight Time, phma@webjockey.net writes: > I am unclear just what "beyond calculation" means here. Not > > apparently, "incalculable," since even my pocket calculator gives values > > for both of these -- approximations, of course, but that suggests that > real > > values are available (though infinitely long, I suppose). Somehow > > inadmissible, like division by 0? But again ... . Such that the > > distinction between fractions and not does not apply? Does any of this > say > > that the presented proof is not a proof? > > I meant "transcendental". What's the right word? > > I don't know the proof; I just saw it stated on Wikipedia. Finding out that > > the number is irrational does not invalidate the proof. > Thanks; I really was unclear about the point. As for the right word, since I forget the difference between irrational and transcendantal, I was happy with {nalfrinu} till now. Now, having three not obviously equivalent definitions of "transcendental" (just in mathematics), I am even less sure. I suppose what fits here it the old infinite non-repeating decimal expansion -- which gives a horrible definition-type lujvo (though not as bad as "neither root nor quotient of rationals" or "not definable by an finite number of rationally coefficiented equations") Time for a good metaphor, which "beyond computing" just may be, though it clearly sets off alarms in many people's belief webs. jay.kominek But this is about transcendental numbers, which, though presumably related, are not quite the same thing: the algebra seems OK here -- unless rational coefficients are required to call it algebra. We don't, of course, have a word for algebra either (nor hardly any other branch of mathematics -- or anything else). greg: <> .i ru'a lo'i namcu poi se skicu do fo zo kajbancu du lo'i namcu poi na'eka'e > pixra zbasu .i xu go'i .i .e'u ri selcme zo nalpirzbana'u> I worry about {pixra zbasu} here, but I suppose the point is "can be pictured" somehow or other. That doesn't seem quite the point, although it is a bit hard to picture some of them, while others work pretty easily: the root-twoth power of root-two doesn't do a thing for me, but pi (surely transcendental if anything is) is just how much you have to stretch the diameter of a circle to wrap it around. But maybe it is a less distracting metaphor (trimmed down a bit). --part1_191.65c92d9.2a01940a_boundary Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: 7bit In a message dated 5/1/2002 9:05:48 AM Central Daylight Time, phma@webjockey.net writes:


I am unclear just what "beyond calculation" means here.  Not
> apparently, "incalculable," since even my pocket calculator gives values
> for both of these -- approximations, of course, but that suggests that real
> values are available (though infinitely long, I suppose).  Somehow
> inadmissible, like division by 0?  But again ... .  Such that the
> distinction between fractions and not does not apply?  Does any of this say
> that the presented proof is not a proof?

I meant "transcendental". What's the right word?

I don't know the proof; I just saw it stated on Wikipedia. Finding out that
the number is irrational does not invalidate the proof.


Thanks; I really was unclear about the point.  As for the right word, since I forget the difference between irrational and transcendantal, I was happy with {nalfrinu} till now.  Now, having three not obviously equivalent definitions of "transcendental" (just in mathematics), I am even less sure.  I suppose what fits here it the old infinite non-repeating decimal expansion  -- which gives a horrible definition-type lujvo (though not as bad as "neither root nor quotient of rationals" or "not definable by an finite number of rationally coefficiented equations")  Time for a good metaphor, which "beyond computing" just may be, though it clearly sets off alarms in many people's belief webs.

jay.kominek
<For what its worth, a transcendental function is one which cannot be
expressed in algebraic terms.>
But this is about transcendental numbers, which, though presumably related, are not quite the same thing: the algebra seems OK here -- unless rational coefficients are required to call it algebra.  We don't, of course, have a word for algebra either (nor hardly any other branch of mathematics -- or anything else).

greg:
<> .i ru'a lo'i namcu poi se skicu do fo zo kajbancu du lo'i namcu poi
na'eka'e
> pixra zbasu .i xu go'i .i .e'u ri selcme zo nalpirzbana'u>

I worry about {pixra zbasu} here, but I suppose the point is "can be pictured" somehow or other.  That doesn't seem quite the point, although it is a bit hard to picture some of them, while others work pretty easily: the root-twoth power of root-two doesn't do a thing for me, but pi (surely transcendental if anything is) is just how much you have to stretch the diameter of a circle to wrap it around.  But maybe it is a less distracting metaphor (trimmed down a bit).


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